I think you've got the right idea. Even if you did put it in your shed, you could put the system in an insulated housing, and use and exhaust fan system to circulate the cooler air from the outside through.
As somebody mentioned, make sure your cool air intake is at the lower portion of the case/housing and the heat exhaust is out the top.
Also, if you're going to be running the ducting anyway, lose the box fans, and condense your housing down. Install 1-2 of these in your exhaust ducting.
http://www.use-enco.com/CGI/INSRIT?PMAKA=325-7358&cm_mmc=Didit-_-SEM-_-GglProd-_-GglProd&003=18299132&010=325-7358&{copy:002}&{copy:004}&{copy:005}&10=325-7358&gclid=CN3sxp3wi7cCFYx_Qgodr2IAKAThis will be far more efficient for the airflow and will ensure that your box fans don't create a positive pressure in the box that could actually hinder cool air from being streamlined THROUGH the system, and rather just creates a funky little vortex of dead airspace in the ducting, trapping most of the head inside your housing.
Use the fans DESIGNED for this type of work, and you'll be happier overall.
Also, if you only have one window to use two halves of for your ducting, make sure to put an elbow that points down on the intake, and a stack to exhaust the hot air up a few inches, so that you're not just recirculating the same hot air back in.
I would avoid a swamp cooler, as humidity and electronics are mortal enemies.
Also, I would put a lot of thought into how you're going to direct airflow THROUGH the system, making the air pass completely through the first level, and then moving up to the second level; orienting components so that they get the best airflow through them, and so that the airflow works with any individual component fans that might be in the system. No offense, but looking at your existing setup, it looks like very little thought was put into how to route the airflow, and instead, a random fan was just pointed anywhere it might be able to fit...
Another option would be to do a water-cooling setup, with a radiator routed outside.
Thank you for your reply.
Moving to an isolated system with fresh air in the bottom and hot air out the top, the boards which the motherboards and box fan sit on would need to be rethought as they are now a barrier to air flow. I can get rid of the wye then also and have one intake and one exhaust. I have separate windows on different walls of the room to use one for intake, one for exhaust. 6" ducting large enough?
Ok getting rid of the box fans is fine but they will need to be replaced as the cards will need some sort of airflow across them I would think. You mention using fans designed for this type of work. Are you suggesting 120mm or something more powerful?